Broadband Dielectric Spectroscopy (BDS)in soft matter research

F.Kremer

The spectrum of electro-magnetic waves

UV/VIS IR Broadband Dielectric Spectroscopy (BDS)

Questions to be addressed:

1. What molecular processes take place in the spectral range fromTHz to mHz and below?

2. What is the principle of Broadband Dielectric Spectroscopy?

3. Excursion: What is the dynamics in a glass?

4. Glassy dynamics in thin polymer layers.

5. Glassy dynamics of semi(isolated) polymer chains

1. What molecular processes take place in thespectral range from THz to mHz and below?

Dcurl H jt

∂= +

∂

0D Eε ε∗= j Eσ ∗=

The linear interaction of electromagnetic fields with matter isdescribed by one of Maxwell‘s equations

(Current-density and the time derivative of D are equivalent)

(Ohm‘s law)

0iσ ωε ε∗ ∗=

( ) iε ω ε ε∗ ′ ′′= − ( ) iσ ω σ σ∗ ′ ′′= +

Basic relations between the complex dielectric function ε* and the complex conductivity σ*

Effect of an electric field on a unpolar atom or molecule:

In an atom or molecule the electron cloud is deformed with respectto the nucleus, which causes an induced polarisation; this response isfast (psec), because the electrons are light-weight

+

-

+

-

-

Electric FieldElectric Field

Effects of an electric field on an electric dipole μ :

An electric field tries to orient a dipole μ; but the thermal fluct-uations of the surrounding heat bath counteract this effect; as result orientational polarisation takes place, its time constant ischaracteristic for the molecular moiety under study and may varybetween 10-12s – 1000s and longer.

-e

+e

Electric field

Effects of an electric field on (ionic) charges:

Charges (electronic and ionic) are Charges (electronic and ionic) are displaced in the direction of theapplied field. The latter gives rise to a resultant polarisation of the sample as a whole.

-

-

-

-

--

-

-

+

+

++

+

+

+ +

Electric fieldElectric field

+

+

+

+

+

+

+

+-

-

-

-

-

-

-

-

What molecular processes take place in the spectralrange from THz to mHz and below?

1. Induced polarisation

2. Orientational polarisation

3. Charge tansport

4. Polarisation at interfaces

2. What is the principle of Broadband Dielectric Spectroscopy?

( )2( )1

sε εε ω ω τω τ

∞−′′ =

+

( )2( )1

sε εε ω ε

ω τ∞

∞

−′ = +

+

*

(1 )s

iε εε ε

ωτ∞

∞−

= ++

2,0

2,4

2,8

3,2

3,6

100 101 102 103 104 105 106

0,0

0,2

0,4

0,6

0,8

ε'=εs

ε'=ε?

Δε=εs-ε?

ε'

ε''max

ωmax

ε''

ω [rad s-1]

0 20 40 60

0

1

2

orientational polarization

induced polarization

Δε = εS- ε00

εS

ε00

ε(t)=

(P(t)

- P

∞) /

ΔE

Time

ΔE

E (t

)Capacitor with N permanent

dipoles, dipole Moment μ

complex dielectric function

Debye relaxation

A closer look at orientational polarization:

P. Debye, Director (1927-1935) of the Physical Institute at the university of Leipzig (Nobelprize in Chemistry 1936)

The counterbalance between thermal and electric ennergy

Capacitor with N permanent Dipoles, Dipole Moment μ

Polarization :∞∞ +=+= ∑ Pμ

VNPμ

V1P i

Mean Dipole Moment

0 20 40 60

0

1

2

orientational polarization

induced polarization

Δε = εS- ε00

εS

ε00

ε(t)=

(P(t)

- P

∞) /

ΔE

Time

ΔE

E (t

)

CH

CH

CH

3

2

3

CO

O

C CH2

Dipole moment

Mean Dipole Moment: Counterbalance

EWel ⋅μ−=kTWth =

Thermal Energy Electrical Energy

∫

∫

π

π

Ω⋅μ

Ω⋅μ

μ

=μ

4

4

d)kT

Eexp(

d)kT

E(expBoltzmann Statistics:

The factor exp(μE/kT) dΩ gives the probability that the dipole moment vector has an orientationbetween Ω and Ω + dΩ.

Spherical Coordinates:

Only the dipole moment component whichis parallel to the direction of the electric field contributes to the polarization θθ

θμ

θθθμ

θμ=μ

∫

∫π

π

dsin21)

kTcosE(exp

dsin21)

kTcosE(expcos

0

0

x = (μ E cos θ) / (kT)a = (μ E) / (kT)

)a(a1

)aexp()aexp()aexp()aexp(

dx)xexp(

dx)xexp(x

a1cos a

a

a

a Λ=−−−−+

==θ

∫

∫

−

−

Langevin function

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0Λ(a)=a/3

Langevin function

a

Λ(a

)

Λ(a)≈a/3 ETk3

2μ=μ

Debye-FormulaVN

Tk31 2

0S

με

=ε−ε ∞

1.0kT

Ea <μ

=

μ<

Tk1.0E

ε0 - dielectric permittivity of vacuum = 8.854 10-12 As V-1 m-1

The Langevin-function

10-2 10-1 100 101 102 103 104 105 106

100

101

102

103

104

105

235 K220 K

205 K

190 K

propylene glycol

ε´´

frequency [Hz]

10-2 10-1 100 101 102 103 104 105 106

100

101

102

103

104

ε´´

frequency [Hz]

Analysis of the dielectric data and ist information content

1. Relaxation time τ and the type of ist thermal activation2. Relaxation time distribution function g(τ) given by

the constants α and γ3. The dielectric strength

²3nkTμεΔ =

Brief summary concerning the principle of BroadbandDielectric Spectroscopy (BDS):

1. BDS covers a huge spectral range from THz to mHz and below.

2. The dielectric funcion and the conductivity are comlex becausethe exitation due to the external field and the response of thesystem under study are not in phase with each other.

3. The real part of the complex dielectric function has thecharacter of a memory function because different dielectricrelaxation proccesses add up with decreasing frequency

4. The sample amount required for a measurement can bereduced to that of isolated molecules.

(With these features BDS has unique advantages compared to otherspectroscopies (NMR, PCS, dynamic mechanic spectroscopy).

3. Excursion: What is the dynamics in a glass?

Single molecule relaxation Liquid-like relaxation(dynamic glass transition)

The temperature dependence of the relaxation rate enables one to distinguish between a single molecule and a liquid-like relaxation.

Dynamic glass transition: a gradual decrease over many ordersof magnitude of the structuralrelaxation time upon cooling.

1000/T [1/K]

The (dynamic) glass transition

2.0 3.0 4.0 5.0

-20

2

4

6

8

-4

-6

10

Calorimetric

Tg

log

(1/τ

)[1/

s]

180 200 220 240 280he

atca

paci

tyC

Temperature /K

Differential scanning calorimetry

Tg

Heat capacity

340 360 380 400 42098

100

102

104

106

108

110

340 360 380 400 420

2.0

2.5

3.0

3.5

C''(ω) [a.u.]

T [K]

C'(ω

) [a.

u.]

Frequency-dependent calorimetry (20 Hz)

Heat capacity320 340 360 380 400

2

2

CT

∂∂

CT

∂∂

C',

C" [

a.u.

]

Temperature /K

0.96

0.97

0.98

0.99

1.00320 340 360 380 400

Tg

C (n

orm

aliz

ed)

(capacitive scanning) dilatometry

Thermal expansion

320 340 360 380 400

1.586

1.578

2

2

( )nT

∂∂

n', n

'' [a.

u.]

Temperature /K

320 340 360 380 400

( )nT

∂∂

Tg

n (λ

=540

nm)

1.570

Ellipsometry

Optical constants n and d

10-1 100 101 102 103 104 105

0.01

240 K235 K230 K225 K220 K215 K

ε''

f [Hz]

Broadband Dielectric Spectroscopy

Molecular motion

Summary concerning glassy dynamics

1. Single-molecule relaxations are Arrhenius-like. Glassy dynamicsis characterized by the empirical Vogel-Fulcher-Tammann (VFT) dependence.

2. The dynamic glass transition is assigned to relaxations between structural substates. It corresponds to a continuous slowing down of the molecular dynamics upon cooling which is usually described by the empirical Vogel-Fulcher-Tammann (VFT) dependence.

3. The dynamic glass transition scales with the calorimetric glass transition. At Tg typically a relaxation rate of .01 Hz is reached.

4. There are manifold ways to measure the dynamic glass transition (Ac- and Dc-calorimetry, dilatometry, viscosimetry, scattering techniques, ellipsometry, Broadband Dielectric Spectroscopy etc). The latter has the advantage that it measures also the relaxation-time distribution.

4. Glassy dynamics in thin polymer layers. a) Literature survey: The (dynamic) glass transition in thin polymer layers and films of

polystyrene (PS)

77 Publications on glassy dynamics in thin layers of PS

60 Publications on glassy dynamics in thin supportedlayers of PS (d = 5 - 50 nm, Mw = 102 – 104 kg/mol)

Many publications and methods find no shift. Divergence islikely due to differences in preparative conditions

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 400

2

4

6

8

10

12

14

16

18 layers suported onsolid substrates (60)

Ellipsometry Brillouin light scattering Broadband Dielectric Spectroscopy (BDS) Differential Scanning Calorimetry (DSC) Fluorescence microscopy X-ray reflectivity AC-calorimetry AFM force spectrocopy Positronium lifetime spectroscopy Rheology Thermal Expansion Spectroscopy Neutron scattering

Num

ber o

f pub

licat

ions

shift in Tg or Tα [K]

74 Publications on glassy dynamics in thin supportedlayers and freestanding films of PS (d = 5 - 50 nm, Mw= 102 – 104 kg/mol)

Huge shifts are observed in freestanding films, which cannot berigorously annealed (remaining solvent)?

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 400

2

4

6

8

10

12

14

16

18 freestanding films (16) Ellipsometry Brillouin light scattering BDS DSC Fluorescence microscopy X-ray reflectivity AFM force spectroscopy Nano-bubble inflation

layers suported onsolid substrates (60)

Ellipsometry Brillouin light scattering Broadband Dielectric Spectroscopy (BDS) Differential Scanning Calorimetry (DSC) Fluorescence microscopy X-ray reflectivity AC-calorimetry AFM force spectrocopy Positronium lifetime spectroscopy Rheology Thermal Expansion Spectroscopy Neutron scattering

Num

ber o

f pub

licat

ions

shift in Tg or Tα [K]

77 Publications on glassy dynamics in thin supportedlayers, freestanding and suspended films of PS (d = 5 -50 nm, Mw = 102 – 104 kg/mol)

Many publications and many methods find no shift. Divergenceis likely due to differences in preparative conditions

-80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 400

2

4

6

8

10

12

14

16

18 freestanding films (16) Ellipsometry Brillouin light scattering BDS DSC Fluorescence microscopy X-ray reflectivity AFM force spectroscopy Nano-bubble inflation

films suspendedon liquids (3)

Ellipsometry BDS Dewetting

(by optical inspection)

layers suported onsolid substrates (60)

Ellipsometry Brillouin light scattering Broadband Dielectric Spectroscopy (BDS) Differential Scanning Calorimetry (DSC) Fluorescence microscopy X-ray reflectivity AC-calorimetry AFM force spectrocopy Positronium lifetime spectroscopy Rheology Thermal Expansion Spectroscopy Neutron scattering

Num

ber o

f pub

licat

ions

shift in Tg or Tα [K]

Summary concerning the literature survey(77 papers on PS)

1. There is a huge spread in the published shifts of theglass transition temperature Tg.

2. It is excluded, that this is a material property of PS. Instead it is indicated, that it is simply an artefact of preparation. It is revealing, that for free standing films - which cannot be thoroughly annealed – Tg shifts of up to -80 K are reported.

3. A majority of experiments and methods finds no shift in Tg (down to thicknesses of 5 nm).

4. Glassy dynamics in thin polymer layers. b) Combined dielectric and ellipsometric studies on

nanometric thin (5nm – ~400nm) PS-layers with widely varying molecular weight (deposited on

Si/SiOx substrates).

n

(1) Dice made of highly doped Si are thoroughly cleaned and thepolymer layer is spincoated on them at 50 rev/sec.

(2) Prior to the dielectric measurement, the films are annealedin high (oil-free) vacuum (~10e-6 mbar) at Tg + 50°C for at least 24 hours.

(3) Before and after a dielectric measurements cycle the surfaceroughness is measured by AFM and compared in order to exclude dewetting.

(4) During the full measurement cycle the sample is kept in high purity nitrogen gas.

Sample preparation procedure for the dielectric and ellipsometric measurements

Rrms = 1.99 nm Rrms = 1.93 nm

The topography of the film surface not is changed during a measurement cycle (~20 hrs)

AFM on the surface topography of a 10-nm thin PS (MW =319 kg/mol) layer, before and after a dielectric

measurement cycle (~20 hrs)Before: After:

Novel approach using nanostructured electrodes avoidsevaporation of metal counterelectrodes

Spacers (SiO2)

Ultra-flat highlyconducting Si wafers

Spin-coatedfilm

110 nm

By that even the dynamics of isolated polymer coils can bemeasured

6 μm45 µm

110 nm

6µm

Serghei, A. and Kremer, F. Rev.Scientific Instruments 77, 116108 (2006)

Full stability and reproducibility is achieved – if the layers are keptin high purity nitrogen or argon gas

Stability and reproducibility of thin PS layersBDS: (MW=1000 kg/mol), thickness 21 nm

Ellipsometry: (MW=319 kg/mol), thickness 52 nm

380 390 400 410 420

Ellipsometry:heating and cooling cycle

0.08kHz 0.5 kHz 2 kHz

log

ε″ne

t

T / K320 360 400 440

53

54

55

T / K

d / n

m

BDS:cooling and heating run beforeand after substantial measurement

1,57

1,58

1,59

n

-5

-4

-3

380 390 400 410 420-5

-4

-3

380 390 400 410 4200,0

0,5

1,0

91 nm 26 nm 21 nm 11 nm

log

ε″ne

t

T / Kε″

net n

orm

.T / K

Dielectric measurements in the nanostructured electrodearrangement of PS layers of varying thickness

(MW =1 103 kg/mol; 1 kHz)

Down to 11nm of PS, no shift in the mean relaxation time isobserved.

Glassy dynamics and glass transition temperature of PS layers (MW =319 kg/mol) of varying thickness as investigated by multiple experimental methods

No shift in the glassy dynamics (±3 K) down to 5 nm as proven by four different techniques

0 20 40 60 80 100

370

372

374

376

378

380 Ellipsometry X-Ray Reflectometry DSC (bulk)

T g / K

d / nm

396

398

400

402

404

406

BDS uncapped BDS capped AC-Calorimetry (bulk)

Tα (f=1 kH

z) / K

PS, Mw = 319 kg/mol

Glassy dynamics and glass transition temperature of

PS layers (~20 nm thick) for varying molecular weight

370372374376

398400402404

No molecular weight dependence in Tg and Tα is observed.

Tg Ellipsometry Tg X-ray reflectometry

Tα BDS uncapped

Tα BDS capped

Tg, T

α [K

]

log (Mw [g/mol])

4 5 6 7

Glassy dynamics and glass transition temperature of PS layers of varying thickness and molecular weight as investigated by multiple

experimental methods

Results of multiple experimental methods coincide over a wide range of mean re-laxation rate.

2,4 2,5 2,6 2,7

-1

0

1

2

3

4

5

ACC, bulk samples 8 090 kg/mol 319 kg/mol

Ellipsometry (SE) 294 nm, 58.9 kg/mol 12 nm, 58.9 kg/mol 246 nm, 8 090 kg/mol 15 nm, 8 090 kg/mol

DSC, bulk samples 8 090 kg/mol 319 kg/mol 58.9 kg/mol

BDS, capped 169 nm, 58.9 kg/mol 37 nm, 58.9 kg/mol corresponding VFT-fit 6 nm, 319 kg/mol 38 nm, 8 090 kg/mol

BDS, uncapped 29 nm, 8 090 kg/mol 9 nm, 8 090 kg/mol

- lo

g (τ

/ s)

1000 / (T / K)

420 410 400 390 380 370 T / K

-2

-1

0

1

2

3

4

log (f / Hz)

4. Conclusions1. In combined dielectric, ellipsometric & calorimetric studies, it is

shown that the glass transition temperature of nanometric PS layers down to 4.8nm is not shifted. The sample preparation was carried independently by three different groups (Dresden, Rostock, Leipzig)

2. No molecular weight dependence in Tg or Tα is observed.

3. In the dielectric spectra no broadening of the relaxation time distribution function is observed.

4. Similar results are obtained for a manifold of other polymers

Mapesa, E.U., Erber, M., Tress, M., Eichhorn, K.-J., Serghei, A., Voit, B. & Kremer, F. Europ. Phys. J. - Special Topics 189, 173-180 (2010), DOI: 10.1140/epjst/e2010-01320-2Tress, M., Erber, M., Mapesa, E.U., Huth, H., Müller, J., Serghei, A., Schick, C., Eichhorn, K.-J., Voit, B. & Kremer, F. Macromolecules 43, 9937-9944 (2010) DOI: 10.1021/ma102031kErber, M., M. Treß, E.U. Mapesa, A. Serghei, K.-J. Eichhorn, B. Voit and F. Kremer Macromolecules 43, 7729 (2010), DOI: 10.1021/ma100912Serghei, A.; H. Huth, C. Schick, F. Kremer, Macromolecules 41 (10), 3636 (2008).

4. Glassy dynamics in thin polymer layers. c) Molecular dynamics of thin layers of

poly(cis-1,4-isoprene) PI

cis-polyisoprene – a type-A polymer(W. H. Stockmayer, Pure Appl. Chem. 1967, 15, 539)

Two relaxation processes probing two different length scales:

Segmental mode (dynamic glass transition):“fluctuation of 2-3 monomer units”(I. Bahar, B. Erman, F. Kremer and E.W. Fischer, Macromolecules 1992, 25, 816)

Normal mode:Fluctuation of the end-to-end distance vector(K. Adachi, T. Kotaka, Macromolecules, 1985, 18, 466, D. Böse and F. Kremer, Macromolecules, 1990, 23, 829)

RE-E

Cis-1,4-polyisoprene in the confinement of thin layers

Samples:

Questions:1. Stability of thin polyisoprene layers2. Scaling of the segmental mode (dynamic glass transition)

with thickness d and molecular weight Mw3. Scaling of the normal mode (fluctuation of the end-to-end

vector) with thickness d and molecular weight Mw4. Relaxation time distribution function of both segmental

and normal mode

Mw [Kg/mol]

Mw/Mn RE-E[nm]

Rg[nm]

11.6 1.06 8.9 3.544.5 1.06 17.4 6.953 1.06 19 7.575 1.08 22.6 9

Are thin (< 20 nm) polyisoprene (PIP) films stable?

before measurement after measurement

Roughnessrms = 1.92 nm Roughnessrms = 1.84 nm

Surface remains unchanged during measurement

200 370K

Mesaurement from200K to 370K, and back to 200K lasting 40 hrs

No hysteresis effects are observed. The PIP layers are perfectly stable.

200 240 280 320 360 4000.000

0.001

0.002

0.003

heating cooling

ε″ne

t

T /K

Mw

= 53 kg/mol; d = 15 nm

f = 80 Hz

200 240 280 320 360 40

0.0002

0.0004

0.0006

0.0008

heating cooling

ε″ne

tT /K

Mw = 53 kg/mol; d = 7 nm

f = 80 Hzsegmentalmode

normalmode

normalmode

segmentalmode

Reproducibility of dielectric measurements?

Glassy dynamics of PIP (45 & 53k) from bulk down to 7 nm

The segmental mode (dynamic glass transition) does not shift in its relaxation rate with reducing thickness; in contrast thenormal mode becomes faster. This proves that the conformationof the chain is changed.

0.000

0.004

0.008

0.012

200 240 280 320 360

0.0

0.5

1.0

ε″ne

t

0 .00

0.01

0.02

0.03

ε″bulk

bulk 369 nm 111 nm 28 nm 15 nm 7 nm

ε″⁄ε″

max

T /K

f = 80 Hz

PIP-53kg/m ol

0.000

0.005

0.010

0.015

200 240 280 320 3600.0

0.2

0.4

0.6

0.8

1.0

PIP-45kg/mol

ε″bulkε″ne

t

f = 80 Hz0.00

0.01

0.02

0.03

bulk 312 nm 116 nm 57 nm 11 nm 7 nm

ε″/ε

″ max

T /K

2 3 4 50

1

2

3

4

5

6

7

8

11.6 kg/mol bulk 327nm

44.5 kg/mol bulk 312 nm 116 nm 57 nm 11 nm 7 nm

53 kg/mol bulk 369 nm 28 nm 15 nm 7 nm

75 kg/mol bulk 326 nm 57 nm 21 nm 17 nm 9 nm

log

[1/τ

(s-1)]

1000/T [K-1]

segmental mode

normal mode for cMw=10kg/mol

Dynamics of PIP: from bulk to ultra-thin layers

Segmental mode independent of d and MwNormal mode varies strongly in dependence to changesin d and Mw

Dynamics of polyisoprene: mean relaxation time distribution of both, the segmental and normal modes

(PIP-45 kg/mol)

200 240 280 320 360

0.0

0.5

1.0

The relaxation time distribution functions reveal an identicalsegmental mode for all thicknesses, and a normal mode thatbecomes faster with reducing thickness

312 nm 116 nm 57nm 7nm

ε″⁄ε″

max

T /K

lines: corresponding model functions

-16 -12 -8 -4 0 40.0

0.2

0.4

0.6

0.8

1.0

312 nm 116 nm 57 nm 7 nm

L(τ)

[a.u

.]log (τ [s])

segmental mode

normalmode

Dynamics of polyisoprene: Havriliak-Negami fit parameters

Fit parameters for the segmental mode hardly vary with d and Mw, but those for the normal mode show a pronounced variation

Segmental mode Normal modecode Thickness (nm) α β Δε α β Δε

PIP-45 bulk31211657117

0.740.720.720.710.700.71

0.450.400.400.410.430.42

0.1380.0680.0380.0140.00760.0026

0.990.550.550.510.550.39

0.400.140.140.100.840.9

0.080.10.04280.01740.00980.0065

PIP-53 bulk36911128157

0.720.710.700.680.690.69

0.490.450.420.430.410.42

0.1210.040.0350.0180.0110.004

0.710.540.540.540.650.28

0.350.150.150.210.300.35

0.0920.0510.0480.0220.0170.011

PIP-75 bulk32657211796

0.730.700.700.700.700.700.70

0.510.400.400.400.400.400.40

0.130.0360.01870.00290.00190.0010.0009

0.630.500.450.470.850.170.17

0.360.140.140.150.150.350.34

0.110.0680.0290.0180.0110.0090.0046

Dynamics of polyisoprene: dieletric strength of segmental (seg. m. ) and normal mode (norm. m.)

10 100

0.00

0.02

0.04

0.06

0.08

0.10

Dielectric strength of both segmental and normal mode reduceswith thickness – reducing number density of fluctuating dipoles

45kg/mol 53kg/mol 75kg/mol

Δεse

g. m

.; Δε

norm

. m.

d / nm

seg. m. norm. m.

Why does the segmental mode (dynamic glasstransition) show no confinement effect (thickness >

5nm) in contrast to the normal mode?

Length scale of 2-3 polymer segments (~ 0.5nm)

(I. Bahar, B. Erman, F. Kremer and E.W. Fischer, Macromolecules 1992, 25, 816)

20-30nm

The dynamic glass transition takes place at the length scaleof 2-3 polymer segments corresponding to ~ 0.5nm. This is stillsmall compared to the extension of the 1-D confinement.But the conformation of the chain changes.

Summary concerning the molecular dynamics and glass transition of poly(cis-1,4-isoprene) PI

1. In PI two relaxation processes are observed, a segmental mode corresponding to the dynamic glass transition and a „normal mode“ being assigned the fluctuation of the „end-to-enddistance“.

2. The segmental mode (dynamic glass transition) is not shiftedwith decreasing thickness (down to 7 nm) for all molecularweights analysed. There is no indication that the relaxation-time distribution function broadens with decreasing layerthickness.

3. The relaxation-time distribution of the normal mode changesstrongly with decreasing layer thickness, proving that theconformation of the chain is altered.

5. Glassy dynamics of semi(isolated) polymer chains poly(2-vinylpyridine) (P2VP).

MW=2.5 * 105 g/mol MW=106 g/mol MW=1.7 * 106 g/mol

1 x 1 µm2 1 x 1 µm2 1 x 1 µm2

0.0 0.5 1.0 1.5 2.0

1

2

3

single chain volume(via mass density)co

il vo

lum

e [1

03 nm

3 ]

molecular weight MW [106 g/mol]

AFM investigation of isolated P2VP polymer coils

The average coil volumecorrelates with themolecular weight and isclose to the single chainvolume.

-1,0

-0,5

0,0

380 390 400 410 420 430-3,4

-3,2

-3,0

-2,8

P2VPMW=1.7*106 g/molFrequency

104 Hz 103 Hz 102 Hz

log

ε''bulk

isolatedcoils

log

ε''

Temperature T [K]

Isolated P2VP polymer coils show clearly a segmental mode and hence a glassy dynamics. Compared to bulk the dynamics is shifted to higher temperatures.

Do isolated polymer coils have a glass transition?

The glassy dynamics of isolated P2VP polyer coils is sloweddown by up to one decade compared to bulk dynamics.

Glassy dynamics of isolated P2VP polymer coils

2,3 2,4 2,5 2,6 2,7-1

0

1

2

3

4

5

6

430 420 410 400 390 380

-1

0

1

2

3

4

5

bulk (measured) isolated coils assuming

bulk dynamics (modelled) isolated coils (measured)

-log(

τ [s

])

1000/T [1/K]

T [K]

log(

f [H

z])

20 30 40 50 60 700,0

0,5

1,0

1,5

2,0

2,5

3,0

2.7 %

10 %

17.7 %

26 %

Hei

ght [

nm]

Lateral extension [nm]

43.6 %

Almost half of the segments are in within a range of .5 nm to the solid substrate.

Total volume:~ 1.7 * 103 nm3

segment volume:~ (0.5 nm)3

The profile of a single P2VP (Mw=1.7 * 1E6 g/mol) ) coil as determined by AFM

Summary concerning the glass transition of isolated P2VP polymer coils.

1. Isolated coils of P2VP exhibit a well defined dynamic glasstransition.

2. The dynamic glass transition is slowed down by up to onedecade compared to bulk dynamics due to interactions withthe solid interface.

Final Conclusions1. Using novel nanostructured electrodes enables one to carry

out broadband dielectric measurements on polymer layersof nanometric thicknesses and below.

2. In combined dielectric & ellipsometric studies, it is shownthat the glass transition temperature of nanometric PS layers down to 4.8nm is not shifted and does not broaden.

3. Similar results are obtained for a multitude of otherpolymers (PMMA, PVAc, etc).

4. For Polyisoprene it is demonstrated that the conformationof the chain changes in dependence on the thickness.

5. Even isolated polymer coils exhibit a dynamic glasstransition.

Controlquestions:

!..

1. What is the principle of Broadband Dielectric Spectroscopy (BDS)?2. What are the „figures of merit“ of BDS?3. What is the information content of dielectric spectra?4. What is the relationship beween Polarisation, Dielectric

Displacement and electric field? 5. What is the relationship between the complex dielectric function and

the complex conductivity?6. What states the Langevin function?7. What states the Debye formula?8. What are the basic assumptions of the Rouse (bead and spring)

model?9. What is the molecular assignment of the dynamics glass transition in

case of low molecular weight and polymeric samples?10. On what length scale does the dynamic glass transition takes place?

Thanks to

DFG (SPP 1369)for finacial support

K.-J. Eichhorn, B. Voit,IPF (Dresden)

C.Schick,(Rostock)